Related papers: On multivariate orderings of some general ordered …
Structural learning of directed acyclic graphs (DAGs) or Bayesian networks has been studied extensively under the assumption that data are independent. We propose a new Gaussian DAG model for dependent data which assumes the observations…
In this work, we consider a diffusive two-species d-dimensional model and study it in great details. Two types of particles, with hard-core, diffuse symmetrically and cross each other. For arbitrary dimensions, we obtain the exact density,…
Structure learning of Gaussian graphical models is an extensively studied problem in the classical multivariate setting where the sample size n is larger than the number of random variables p, as well as in the more challenging setting when…
Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction. However, the extreme complexity of natural…
Bayesian networks are a powerful framework for studying the dependency structure of variables in a complex system. The problem of learning Bayesian networks is tightly associated with the given data type. Ordinal data, such as stages of…
In this paper, we studied the stochastic ordering behavior of series as well as parallel systems' lifetimes comprising dependent and heterogeneous components, experiencing random shocks, and exhibiting distinct dependency structures. We…
Ordinal regression falls between discrete-valued classification and continuous-valued regression. Ordinal target variables can be associated with ranked random variables. These random variables are known as order statistics and they are…
Ordered categorical data frequently arise in the analysis of biomedical, agricultural, and social sciences data. The logistic regression model is attractive in analyzing ordered categorical data because of its use in interpretation of a…
Two classifications of second order ODE's cubic with respect to the first order derivative are compared in the case of general position, which is common for both classifications. The correspondence of vectorial, pseudovectorial, scalar, and…
We consider the problem of computing the joint distribution of order statistics of stochastically independent random variables in one- and two-group models. While recursive formulas for evaluating the joint cumulative distribution function…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
An extension of Archimax copula class in more than two random variables ( Multivariate ) was introduced in (J\'agr 2011) for describing dependency structures among random variables in higher dimension, and some properties of Archimax copula…
Biased sampling designs can be highly efficient when studying rare (binary) or low variability (continuous) endpoints. We consider longitudinal data settings in which the probability of being sampled depends on a repeatedly measured…
Let $X_1, X_2,\ldots, X_n$ (resp. $Y_1, Y_2,\ldots, Y_n$) be independent random variables such that $X_i$ (resp. $Y_i$) follows generalized exponential distribution with shape parameter $\theta_i$ and scale parameter $\lambda_i$ (resp.…
The second-largest order statistic is of special importance in reliability theory since it represents the time to failure of a $2$-out-of-$n$ system. Consider two $2$-out-of-$n$ systems with heterogeneous random lifetimes. The lifetimes are…
Ordinal regression is a classification task where classes have an order and prediction error increases the further the predicted class is from the true class. The standard approach for modeling ordinal data involves fitting parallel…
We consider the problem of sequential learning from categorical observations bounded in [0,1]. We establish an ordering between the Dirichlet posterior over categorical outcomes and a Gaussian posterior under observations with N(0,1) noise.…
We investigate the spectral properties of a generalized GOE (Gaussian Orthogonal Ensemble) capable of describing critical statistics. The joint distribution of eigenvalues of this model is expressed as the diagonal element of the density…
Direct Statistical Simulation (DSS) solves the equations of motion for the statistics of turbulent flows in place of the traditional route of accumulating statistics by Direct Numerical Simulation (DNS). That low-order statistics usually…
As the unification of various models of ordered quantities, generalized order statistics act as a simplistic approach introduced in \cite{kamps1995concept}. In this present study, results pertaining to the expressions of marginal and joint…